Without any exception, the Coriolis force mass flowmeter being marketed at the present time commands very high prices starting from 5,000 dollars and up depending on the size of the flowmeter. One of the co-inventors of the present invention has invented an electronic data processing method for determining the mass flow rate of media as a linear function of ratio of two values of a first alternating electrical signal representing the flexural vibration of the conduit at a first section thereof respectively measured at two instants when a second alternating electrical signal representing the flexural vibration of the conduit at a second section thereof reaches a zero value and a peak value (U.S. Pat. No. 5,184,518), which data processing method can be executed by a very inexpensive data processor costing no more than 50 to 100 dollars in contrast to the 2,500 to 3,000 dollar data processor available at the present time. A highly accurate and very inexpensive Coriolis force mass flowmeter can be provided when the above-mentioned inexpensive data processor is combined with an inexpensive mechanical sensor of the Coriolis force flowmeter. The major portion of the manufacturing cost of the existing versions of the mechanical sensor in the Coriolis force flowmeter results from the assembly employing a matched pair of vibrating conduits and the fittings connecting the pair of vibrating conduits to the common inlet and the common outlet of the flowmeter. A mechanical sensor of the Coriolis force flowmeter employing a single vibrating conduit can be manufactured at a fraction of the cost required to manufacture the existing versions employing the matched pair of vibrating conduit. When a mechanical sensor of the Coriolis force flowmeter employing a single vibrating conduit is combined with the simple and inexpensive electronic data processor executing the method disclosed in U.S. Pat. No. 5,184,518, the cost of the Coriolis force flowmeter can be brought down from the existing price of 5,000 dollars and up to 1,500 to 3,000 dollars range.